There are many Orthodox monasteries in Greece. The area that has many monasteries and enjoys autonomous status but allows only men to enter is called Agion Oros aka Mount Athos.
If you are an international tourist looking for a place with religious significance combined with natural landscape beauty, then my suggestion for you is to visit the suspended rocks - Meteora. As a matter of fact, one of the 007 James Bond movies was filmed in Meteora.
However if you have very limited time, and you happen to be near Nafplio or Mycenae, then you may just want to visit some monastery nearby. In this case, there are many monasteries in Peloponnisos in the mountain range of Parnonas Πάρνωνας. Parnonas are called by many as the Agion Oros of southern Greece.
The most visited monastery in this region is the Monastery of Malevi or in Greek Ιερά Μονή Παναγίας Μαλεβής, it is between the road from the town of Astros to the village of Agios Petros but close to the latter. I have visited that monastery a few times, and have taken many pictures but since other people have posted on the internet, I see no urgency to document my photos.
This is a new landmark on the road to the monastery, after here the road leads solely to the monastery and no where else
zoom in to an icon of mother Mary and infant Christ
the entrance to the monastery's courtyard
nuns always maintain the monastery's garden well
the rear view blocked by the wall
the whole compound from the rear
chestnut trees are just outside the monastery
also found near are the pomegranate trees, in Greek this fruit is called ρόδι
As you can see monasteries are often built in remote mountain areas because the nuns or monks want quietness to approach God by worshiping and praying, the road shown in the picture is an unpaved road, an alternative way to reach the monastery if you have a jeep
this is a small church structure at a lookout point not far from the monastery
Overlooking the town of Astros, whereas the far-away hill to the right is Paralio Astros
To see all the photos for the Monastery Paleopanagia near Astros, go to this link.